Chemical front and flame front propagation in Hele-Shaw cells

View on-line presentation on aqueous chemical fronts in Hele-Shaw cells
View on-line presentation on gaseous flames in Hele-Shaw cells
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It is well known that buoyancy and thermal expansion affect the propagation rates and shapes of premixed gas flames. The understanding of such effects is complicated by the large density ratio between the reactants and products, which induces a baroclinic production of vorticity due to misalignment of density and pressure gradients at the front, which in turn leads to a complicated multi-dimensional flame/flow interaction. The Hele-Shaw cell, i.e., the region between closely-spaced flat parallel plates, is probably the simplest system in which multi-dimensional convection is present, consequently, the behavior of fluids in this system has been studied extensively (Homsy, 1987). Probably the most important characteristic of Hele-Shaw flows is that when the Reynolds number based on gap width is sufficiently small, the Navier-Stokes equations averaged over the gap reduce to a linear relation, namely a Laplace equation for pressure (Darcy's law).

In this work, flame propagation in Hele-Shaw cells is studied to obtain a better understanding of buoyancy and thermal expansion effects on premixed flames. This work is also relevant to the study of unburned hydrocarbon emissions produced by internal combustion engines since these emissions are largely a result of the partial burning or complete flame quenching in the narrow, annular gap called the "crevice volume" between the piston and cylinder walls (see, for example, the text by J. B. Heywood, 1988). A better understanding of how flames propagate in these volumes through experiments using Hele-Shaw cells could lead to identification of means to reduce these emissions.

Because of the very weak thermal expansion (typically 0.06%) caused by chemical reaction, the aqueous chemical fronts are affected by buoyancy. This phenomenon has been studied in Hele-Shaw cells, i.e., the gap between two closely spaced flat parallel plates. Results show a new type of fingering mechanism not present in non-reacting Hele-Shaw flows, which has been identified as a surface tension effect, even though the reactant and product solutions are miscible in all proportions. In fact, this wavelength is almost independent of the front propagation speed (S or S_L) and the cell thickness (w). The only viable explanation of this, when compared to the predictions of the Saffman-Taylor model, is a surface tension at the interface whose magnitude is about 0.005 dyne/cm – about 14,000 times smaller than that of a water-air interface.

Left: images of upward propagating autocatalytic fronts in a Hele-Shaw cell, cell thickness (w) = 1.0 mm, S_L = 0.17 mm/s. Upper image: 10 seconds after initiation; lower image: after reaching quasi-steady propagation condition. Width of cell is 200 mm. Right: effect of w and S_L (Peclet number = Sw/D, where D = mass diffusivity of the stoichiometrically limiting reactant, IO₃^-) on wavelength of initial disturbance.

Remarkably, the propagation rates of these wrinkled buoyant fronts also conform to Yakhot's predictions when a characteristic linear growth rate of the buoyancy-induced instability is used to estimate the effective turbulence intensity (see second plot on this page).

As a complement to the experiments on chemical fronts in Hele-Shaw cells, premixed-gas flames in Hele-Shaw cells were also examined. Significantly, wrinkling was observed even for downward propagating (buoyantly stable) flames and flames having high Lewis number (diffusive-thermally stable). The burning rates (S_T) of these flames are quite different from their laminar, unwrinkled values (S_L). Values of S_T/S_L in the quasi-steady stage were higher for upward vs. downward propagation, but only weakly dependent on Lewis and Peclet number. Due to these wrinkling effects, the front propagation rates in Hele-Shaw cells are found to be always faster than the laminar flame speed, typically by a factor of 3.These results show that even for diffusively stable mixtures, at microgravity thermal expansion and viscosity changes across the front will lead to flame instabilities. These results also indicate that the behavior of flame propagation in narrow channels such as crevice volumes in premixed-charge internal combustion engines (the source of most unburned hydrocarbon emissions) may be quite different from that inferred from simple laminar flame experiments.

Characteristics of flames in Hele-Shaw cells. Left: direct images (flames propagate from left to right.) Cell width (vertical direction in these images) 39 cm. Cell length (horizontal direction in these images) 60 cm, but images are cropped to show only flame front. Images from left to right: 7.2% CH₄ in air, horizontal propagation; 7.1% CH₄ in air, upward propagation; 7.1% CH₄ in air, downward propagation; 3.0% C₃H₈ in air, horizontal propagation. Right: correlation of wrinkled front speed (S_T/S_L) with Peclet number.